{"id":1978,"date":"2024-06-26T22:42:23","date_gmt":"2024-06-26T22:42:23","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1978"},"modified":"2025-08-15T02:56:27","modified_gmt":"2025-08-15T02:56:27","slug":"mastering-polynomial-functions-theorems-zeros-and-applications-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/mastering-polynomial-functions-theorems-zeros-and-applications-apply-it-1\/","title":{"raw":"Zeros of Polynomial Functions: Apply It 1","rendered":"Zeros of Polynomial Functions: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Use the Remainder Theorem to evaluate polynomials and apply the Factor Theorem to find roots.<\/li>\r\n \t<li>Apply the Rational Zero Theorem and Descartes' Rule of Signs to identify possible rational zeros and estimate the number of positive and negative real zeros.<\/li>\r\n \t<li>Find zeros of polynomial functions and use the Linear Factorization Theorem to construct polynomials.<\/li>\r\n \t<li>Solve real-life problems using polynomial equations.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p class=\"whitespace-pre-wrap break-words\">A renowned architectural firm is designing a series of curved glass panels for a modern building facade.<\/p>\r\n\r\n\r\n[caption id=\"attachment_7132\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-7132\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-300x195.jpg\" alt=\"\" width=\"500\" height=\"325\" \/> A roof of curved glass panels; Photo by Daniel Watson on Pexels[\/caption]\r\n<p class=\"whitespace-pre-wrap break-words\">The panels need to follow specific polynomial functions to create both aesthetically pleasing curves and meet structural engineering requirements. The firm's engineers must analyze these polynomial functions to ensure proper design and installation.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31637[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31638[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31639[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31642[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]31641[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Use the Remainder Theorem to evaluate polynomials and apply the Factor Theorem to find roots.<\/li>\n<li>Apply the Rational Zero Theorem and Descartes&#8217; Rule of Signs to identify possible rational zeros and estimate the number of positive and negative real zeros.<\/li>\n<li>Find zeros of polynomial functions and use the Linear Factorization Theorem to construct polynomials.<\/li>\n<li>Solve real-life problems using polynomial equations.<\/li>\n<\/ul>\n<\/section>\n<p class=\"whitespace-pre-wrap break-words\">A renowned architectural firm is designing a series of curved glass panels for a modern building facade.<\/p>\n<figure id=\"attachment_7132\" aria-describedby=\"caption-attachment-7132\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-7132\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-300x195.jpg\" alt=\"\" width=\"500\" height=\"325\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-300x195.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-1024x666.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-768x500.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-1536x999.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-2048x1332.jpg 2048w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-65x42.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-225x146.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/06\/08162809\/pexels-daniel-watson-90038-1487154-350x228.jpg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-7132\" class=\"wp-caption-text\">A roof of curved glass panels; Photo by Daniel Watson on Pexels<\/figcaption><\/figure>\n<p class=\"whitespace-pre-wrap break-words\">The panels need to follow specific polynomial functions to create both aesthetically pleasing curves and meet structural engineering requirements. The firm&#8217;s engineers must analyze these polynomial functions to ensure proper design and installation.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31637\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31637&theme=lumen&iframe_resize_id=ohm31637&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31638\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31638&theme=lumen&iframe_resize_id=ohm31638&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31639\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31639&theme=lumen&iframe_resize_id=ohm31639&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31642\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31642&theme=lumen&iframe_resize_id=ohm31642&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm31641\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=31641&theme=lumen&iframe_resize_id=ohm31641&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":33,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":206,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1978"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":13,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1978\/revisions"}],"predecessor-version":[{"id":7777,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1978\/revisions\/7777"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/206"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1978\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1978"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1978"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1978"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}